The universe if probably littered with the one-planet graves of cultures which made the sensible economic decision that there's no good reason to go into space -- each discovered, studied, and remembered by the ones who made the irrational decision.Parenthetically, there is the ever-present misunderstanding of what rationality means. Rationality just requires us to have complete preferences that don't loop. It's very easy to do and there is nothing that says we can't decide our goal is space exploration and that goal trumps immediate poverty reduction and so forth, at which point the expense becomes perfectly rational.
Also parenthetically, there is no reason to assume that, even if space exploration is irrational for us (by which we mean that given our constraints we maximize utility by not going into space) that does not mean that it would not be rational for another people with our same preferences but different constraints to go into space.
Now that that's out of the way, imagine that there is a reason that the survival of any species depends on space exploration. There are certainly enough demographic/environmental stories around to fit the bill. The species that survive share one of several characteristics: lower costs of space exploration, political systems that allow for swift public action, mad/visionary multi-multi-multi-billionaires, ... what else?
I'm now fascinated pondering factors that would lower the costs of space exploration. Aside from the existence of materials and ability to produce space-minded scientists, there could be: solar systems where the planets are a little closer together so that nearby planets are more hospitable to life and easier to reach, closer other solar systems to shoot for, longer life spans so that the journey does not impose as great a cost, proximity to other space-faring life who allow exchange of knowledge....
Paradoxically, survival might improve if the looming disaster is more obvious and certain.
Baker gives us a more in depth take on the real economics of space, discussing the economic viability of the industrial mining of space objects, the demand elasticity of space exploration ("It's only at prices of around $100,000/tonne that the market will become highly elastic and revenues will sharply increase.") and why unaided markets alone are unlikely to resolve the problem.
Or, if you'd rather, spend a few minutes pondering French existentialism in a Star Wars setting below the fold (HT: Grandiloquent Bloviator):